Weather forecasts, seasonal forecasts, and climate projections can help their users make good decisions. It has recently been shown that when the decisions include the question of whether to act now or wait for the next forecast, even better decisions can be made if information describing potential forecast changes is also available. In this article, we discuss another set of situations in which forecast change information can be useful, which arise when forecast users need to decide which of a series of lagged forecasts to use. Motivated by these potential applications of forecast change information, we then discuss a number of ways in which forecast change information can be presented, using ECMWF reforecasts and corresponding observations as illustration. We first show metrics that illustrate changes in forecast values, such as average sizes of changes, probabilities of changes of different sizes, and percentiles of the distribution of changes, and then show metrics that illustrate changes in forecast skill, such as increase in average skill and probabilities that later forecasts will be more accurate. We give four illustrative numerical examples in which these metrics determine which of a series of lagged forecasts to use. In conclusion, we suggest that providers of weather forecasts, seasonal forecasts, and climate projections might consider presenting forecast change information, in order to help forecast users make better decisions.

The accurate prediction of extreme weather events is an important and challenging task, and has typically relied on numerical simulations of the atmosphere. Here, we combine insights from numerical forecasts with recent developments in dynamical systems theory, which describe atmospheric states in terms of their persistence (θ−1) and local dimension (d), and inform on how the atmosphere evolves to and from a given state of interest. These metrics are intuitively linked to the intrinsic predictability of the atmosphere: a highly persistent, low-dimensional state will be more predictable than a low-persistence, high-dimensional one. We argue that θ−1 and d, derived from reanalysis sea level pressure (SLP) and geopotential height (Z500) fields, can provide complementary predictive information for mid-latitude extreme weather events. Specifically, signatures of regional extreme weather events might be reflected in the dynamical systems metrics, even when the actual extreme is not well-simulated in numerical forecasting systems. We focus on cold spells in the Eastern Mediterranean, and particularly those associated with snow cover in Jerusalem. These rare events are systematically associated with Cyprus Lows, which are the dominant rain-bearing weather system in the region. In our analysis, we compare the ‘cold spell Cyprus Lows’ to other ‘regular’ Cyprus Low days. Significant differences are found between cold spells and ‘regular’ Cyprus Lows from a dynamical systems perspective. When considering SLP, the intrinsic predictability of cold spells is lowest hours before the onset of snow. We find that the cyclone’s location, depth and magnitude of air-sea fluxes play an important role in determining its intrinsic predictability. The dynamical systems metrics computed on Z500 display a different temporal evolution to their SLP counterparts, highlighting the different characteristics of the atmospheric flow at the different levels. We conclude that the dynamical systems approach, although sometimes challenging to interpret, can complement conventional numerical forecasts and forecast skill measures, such as model spread and absolute error. This methodology outlines an important avenue for future research, which can potentially be fruitfully applied to other regions and other types of weather extremes.

Skillful forecasts of extreme weather events have a major socioeconomic relevance. Here, we compare two complementary approaches to diagnose the predictability of extreme weather: recent developments in dynamical systems theory and numerical ensemble weather forecasts. The former allows us to define atmospheric configurations in terms of their persistence and local dimension, which provides information on how the atmosphere evolves to and from a given state of interest. These metrics may be used as proxies for the intrinsic predictability of the atmosphere, which only depends on the atmosphere's properties. Ensemble weather forecasts provide information on the practical predictability of the atmosphere, which partly depends on the performance of the numerical model used. We focus on heat waves affecting the eastern Mediterranean. These are identified using the climatic stress index (CSI), which was explicitly developed for the summer weather conditions in this region and differentiates between heat waves (upper decile) and cool days (lower decile). Significant differences are found between the two groups from both the dynamical systems and the numerical weather prediction perspectives. Specifically, heat waves show relatively stable flow characteristics (high intrinsic predictability) but comparatively low practical predictability (large model spread and error). For 500 hPa geopotential height fields, the intrinsic predictability of heat waves is lowest at the event's onset and decay. We relate these results to the physical processes governing eastern Mediterranean summer heat waves: adiabatic descent of the air parcels over the region and the geographical origin of the air parcels over land prior to the onset of a heat wave. A detailed analysis of the mid-August 2010 record-breaking heat wave provides further insights into the range of different regional atmospheric configurations conducive to heat waves. We conclude that the dynamical systems approach can be a useful complement to conventional numerical forecasts for understanding the dynamics and predictability of eastern Mediterranean heat waves.

Users of meteorological forecasts are often faced with the question of whether to make a decision now, on the basis of the current forecast, or to wait for the next and, it is hoped, more accurate forecast before making the decision. Following previous authors, we analyze this question as an extension of the well-known cost-loss model. Within this extended cost-loss model, the question of whether to decide now or to wait depends on two specific aspects of the forecast, both of which involve probabilities of probabilities. For the special case of weather and climate forecasts in the form of normal distributions, we derive a simple simulation algorithm, and equivalent analytical expressions, for calculating these two probabilities. We apply the algorithm to forecasts of temperature and find that the algorithm leads to better decisions in most cases relative to three simpler alternative decision-making schemes, in both a simulated context and when we use reforecasts, surface observations, and rigorous out-of-sample validation of the decisions. To the best of our knowledge, this is the first time that a dynamic multistage decision algorithm has been demonstrated to work using real weather observations. Our results have implications for the additional kinds of information that forecasters of weather and climate could produce to facilitate good decision-making on the basis of their forecasts.

Ensemble weather forecasts enable a measure of uncertainty to be attached to each forecast, by computing the ensemble's spread. However, generating an ensemble with a good spread-error relationship is far from trivial, and a wide range of approaches to achieve this have been explored-chiefly in the context of numerical weather prediction models. Here, we aim to transform a deterministic neural network weather forecasting system into an ensemble forecasting system. We test four methods to generate the ensemble: random initial perturbations, retraining of the neural network, use of random dropout in the network, and the creation of initial perturbations with singular vector decomposition. The latter method is widely used in numerical weather prediction models, but is yet to be tested on neural networks. The ensemble mean forecasts obtained from these four approaches all beat the unperturbed neural network forecasts, with the retraining method yielding the highest improvement. However, the skill of the neural network forecasts is systematically lower than that of state-of-the-art numerical weather prediction models.

A probabilistic machine learning method is applied to icing related production loss forecasts for wind energy in cold climates. The employed method, called quantile regression forests, is based on the random forest regression algorithm. Based on the performed tests on data from four Swedish wind parks available for two winter seasons, it has been shown to produce valuable probabilistic forecasts. Even with the limited amount of training and test data that were used in the study, the estimated forecast uncertainty adds more value to the forecast when compared to a deterministic forecast and a previously published probabilistic forecast method. It is also shown that the output from a physical icing model provides useful information to the machine learning method, as its usage results in an increased forecast skill when compared to only using Numerical Weather Prediction data. A potential additional benefit in machine learning for some stations was also found when using information in the training from other stations that are also affected by icing. This increases the amount of data, which is otherwise a challenge when developing forecasting methods for wind energy in cold climates.

To extract the most information from an ensemble forecast, users would need to consider the possible impacts of every member in the ensemble. However, not all users have the resources to do this. Many may opt to consider only the ensemble mean and possibly some measure of spread around the mean. This provides little information about potential worst-case scenarios. We explore different methods to extract worst-case scenarios from an ensemble forecast, for a given definition of severity of impact: taking the worst member of the ensemble, calculating the mean of the N worst members, and two methods that use a statistical tool known as directional component analysis (DCA). We assess the advantages and disadvantages of the four methods in terms of whether they produce spatial worst-case scenarios that are not overly sensitive to the finite size and randomness of the ensemble or small changes in the chosen geographical domain. The methods are tested on synthetic data and on temperature forecasts from ECMWF. The mean of the N worst members is more robust than the worst member, while the DCA-based patterns are more robust than either. Furthermore, if the ensemble variability is well described by the covariance matrix, the DCA patterns have the statistical property that they are just as severe as those from the other two methods, but more likely. We conclude that the DCA approach is a tool that could be routinely applied to extract worst-case scenarios from ensemble forecasts.

Creating spatially coherent rainfall patterns with high temporal resolution from data with lower temporal resolution is necessary in many geoscientific applications. From a statistical perspective, this presents a high- dimensional, highly underdetermined problem. Recent advances in machine learning provide methods for learning such probability distributions. We test the usage of generative adversarial networks (GANs) for estimating the full probability distribution of spatial rainfall patterns with high temporal resolution, conditioned on a field of lower temporal resolution. The GAN is trained on rainfall radar data with hourly resolution. Given a new field of daily precipitation sums, it can sample scenarios of spatiotemporal patterns with sub-daily resolution. While the generated patterns do not perfectly reproduce the statistics of observations, they are visually hardly distinguishable from real patterns. Limitations that we found are that providing additional input (such as geographical information) to the GAN surprisingly leads to worse results, showing that it is not trivial to increase the amount of used input information. Additionally, while in principle the GAN should learn the probability distribution in itself, we still needed expert judgment to determine at which point the training should stop, because longer training leads to worse results.

Weather and climate prediction is dominated by high dimensionality, interactions on many different spatial and temporal scales and chaotic dynamics. This makes many problems in the field quite complex ones, and also state-of-the-art numerical models are - despite their immense computational costs - not sufficient for many applications. Therefore, it is appealing to use emerging new technologies such as artificial intelligence to tackle these problems.

We show that it is possible to use deep neural networks to emulate the full dynamics of a strongly simplified general circulation model, providing both good forecasts of the model state several days ahead as well as stable long-term climate timeseries. This method partly also works on more complex and realistic models, but only for forecasting the model's weather several days ahead, not for creating climate runs. It is sufficient to use 50-100 years of data for training the networks. The same neural network method can be combined with singular value decomposition from numerical ensemble weather forecasting in order to generate probabilistic ensemble forecasts with the neural networks.

On a more fundamental level, we show that in a simple dynamical systems setting there seem to be limitations in the ability of feed-forward neural networks to generalize to new regions of the system. This is caused by different parts of the network learning to model different parts of the system. Contradictory, for another simple dynamical system this is shown not to be an issue, raising doubts on the usefulness of results from simple models in the context of more complex ones. Additionally, we show that neural networks are to some extent able to “learn” the influence of slowly changing external forcings on the dynamics of the system, but only given broad enough forcing regimes.

Finally, we present a method to complement operational weather forecasts. Given the initial fields and the error of past weather forecasts, a neural network is used to predict the uncertainty in new forecasts, given only the initial field of the new forecast.

Data-driven approaches, most prominently deep learning, have become powerful tools for prediction in many domains. A natural question to ask is whether data-driven methods could also be used to predict global weather patterns days in advance. First studies show promise but the lack of a common data set and evaluation metrics make intercomparison between studies difficult. Here we present a benchmark data set for data-driven medium-range weather forecasting (specifically 3-5 days), a topic of high scientific interest for atmospheric and computer scientists alike. We provide data derived from the ERA5 archive that has been processed to facilitate the use in machine learning models. We propose simple and clear evaluation metrics which will enable a direct comparison between different methods. Further, we provide baseline scores from simple linear regression techniques, deep learning models, as well as purely physical forecasting models. The data set is publicly available at and the companion code is reproducible with tutorials for getting started. We hope that this data set will accelerate research in data-driven weather forecasting.